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- W2051234010 abstract "Les problèmes d'élimination peuvent être résolus avec une faible complexité booléenne, à condition d'utiliser des structures de données adéquates pour représenter les polynômes (à savoir des calculs d'évaluation). Cette complexité est polynomiale en la taille des entrées et d'invariants intrinsèques de type degré et hauteur. De plus, cette dépendance en la hauteur disparaît si cette représentation en évaluation est étendue aux entiers. De notre borne supérieure découle, via un théorème des zéros effectif, une borne inférieure à la Liouville de la hauteur logarithmique des approximations diophantiennes des points de la variété. Nous considérons enfin les conséquences pour la résolution pratique des systèmes d'équations polynomiales. Solving elimination problems requires only a moderate amount of bit operations if one uses appropriate data structures (as e.g. straight-line programs) for the encoding of polynomials. We present an elimination procedure whose bit complexity is polynomial in the input size and in the value of two suitably defined invariants which reflect the geometric degree and the arithmetic height of the input system. From our complexity bound we deduce by means of an appropriate effective Nullstellensatz a multivariate and intrinsic version of Liouville's classical theorem on approximation of algebraic numbers by rationals. Consequences for practically solving systems of polynomial equations are drawn." @default.
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- W2051234010 date "1997-12-01" @default.
- W2051234010 modified "2023-10-01" @default.
- W2051234010 title "Le rôle des structures de données dans les problèmes d'élimination" @default.
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- W2051234010 doi "https://doi.org/10.1016/s0764-4442(97)83558-6" @default.
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